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Jun 29, 2018
06/18

by
Thorsten Hohage; Frederic Weidling

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We describe a general strategy for the verification of variational source condition by formulating two sufficient criteria describing the smoothness of the solution and the degree of ill-posedness of the forward operator in terms of a family of subspaces. For linear deterministic inverse problems we show that variational source conditions are necessary and sufficient for convergence rates slower than the square root of the noise level. A similar result is shown for linear inverse problems with...

Topics: Numerical Analysis, Mathematics

Source: http://arxiv.org/abs/1603.05133

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Jun 30, 2018
06/18

by
René Weidling; Jürgen Blum

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The bouncing barrier, a parameter combination at which dust particles in the protoplanetary disk always rebound in mutual collisions, is one of the crucial steps of planet formation. In the past years, several experiments have been performed to determine the mass and velocity regimes at which perfect bouncing does occur and those where there is a chance of the aggregates sticking together. We conducted a microgravity experiment, which allows us to investigate free collisions of millimeter-sized...

Topics: Earth and Planetary Astrophysics, Astrophysics

Source: http://arxiv.org/abs/1412.3236

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Jun 27, 2018
06/18

by
Thorsten Hohage; Frederic Weidling

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This paper is concerned with the classical inverse scattering problem to recover the refractive index of a medium given near or far field measurements of scattered time-harmonic acoustic waves. It contains the first rigorous proof of (logarithmic) rates of convergence for Tikhonov regularization under Sobolev smoothness assumptions for the refractive index. This is achieved by combining two lines of research, conditional stability estimates via geometrical optics solutions and variational...

Topics: Numerical Analysis, Mathematics

Source: http://arxiv.org/abs/1503.05763

Entry card for Hill, Jeanette Weidling for the 1933 May Show. The May Show was a juried exhibition of Northeast Ohio artists held at the Cleveland Museum of Art from 1919 to 1993.

Topics: Cleveland Museum of Art, May Show

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Nov 2, 2010
11/10

by
Weidling, Philip, 1905-

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Jun 28, 2018
06/18

by
Frederic Weidling; Thorsten Hohage

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This paper is concerned with the inverse problem to recover the scalar, complex-valued refractive index of a medium from measurements of scattered time-harmonic electromagnetic waves at a fixed frequency. The main results are two variational source conditions for near and far field data, which imply logarithmic rates of convergence of regularization methods, in particular Tikhonov regularization, as the noise level tends to $0$. Moreover, these variational source conditions imply conditional...

Topics: Numerical Analysis, Mathematics

Source: http://arxiv.org/abs/1512.06586

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Sep 23, 2013
09/13

by
René Weidling; Carsten Güttler; Jürgen Blum

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Over the past years the processes involved in the growth of planetesimals have extensively been studied in the laboratory. Based on these experiments, a dust-aggregate collision model was developed upon which computer simulations were based to evaluate how big protoplanetary dust aggregates can grow and to analyze which kinds of collisions are relevant in the solar nebula and are worth further studies in the laboratory. The sticking threshold velocity of millimeter-sized dust aggregates is such...

Source: http://arxiv.org/abs/1105.3909v2

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Sep 21, 2013
09/13

by
René Weidling; Carsten Güttler; Jürgen Blum; Frithjof Brauer

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To study the evolution of protoplanetary dust aggregates, we performed experiments with up to 2600 collisions between single, highly-porous dust aggregates and a solid plate. The dust aggregates consisted of spherical SiO$_2$ grains with 1.5$\mu$m diameter and had an initial volume filling factor (the volume fraction of material) of $\phi_0=0.15$. The aggregates were put onto a vibrating baseplate and, thus, performed multiple collisions with the plate at a mean velocity of 0.2 m s$^{-1}$. The...

Source: http://arxiv.org/abs/0902.3082v1

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Sep 23, 2013
09/13

by
Eike Beitz; Carsten Güttler; René Weidling; Jürgen Blum

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The formation of planetesimals in the early Solar System is hardly understood, and in particular the growth of dust aggregates above millimeter sizes has recently turned out to be a difficult task in our understanding [Zsom et al. 2010, A&A, 513, A57]. Laboratory experiments have shown that dust aggregates of these sizes stick to one another only at unreasonably low velocities. However, in the protoplanetary disk, millimeter-sized particles are known to have been ubiquitous. One can find...

Source: http://arxiv.org/abs/1105.3897v2

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Sep 22, 2013
09/13

by
Stefan Kothe; Jürgen Blum; René Weidling; Carsten Güttler

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We conducted micro-gravity experiments to study the outcome of collisions between sub-mm-sized dust agglomerates consisting of \mu m-sized SiO2 monomer grains at velocities of several cm/s. Prior to the experiments, we used X-ray computer tomography (nano-CT) imaging to study the internal structure of these dust agglomerates and found no rim compaction so that their collision behavior is not governed by preparation-caused artefacts. We found that collisions between these dust aggregates can...

Source: http://arxiv.org/abs/1302.5532v2